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{{DISPLAYTITLE:Geary's ''C''}}
{{multiple issues|primarysources = March 2013|refimprove = March 2013|original research = March 2013}}
'''Geary's ''C''''' is a measure of spatial autocorrelation. Like temporal [[autocorrelation]], spatial autocorrelation means that adjacent observations of the same phenomenon are correlated. However, temporal [[autocorrelation]] is about proximity in time, while spatial autocorrelation is about proximity in (multi-dimensional) space. Spatial autocorrelation is more complex than [[autocorrelation]] because the correlation is multi-dimensional and bi-directional.


Geary's ''C'' is defined as


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:<math> C = \frac{(N-1) \sum_{i} \sum_{j} w_{ij} (X_i-X_j)^2}{2W \sum_{i}(X_i-\bar X)^2} </math>
 
where <math>N</math> is the number of spatial units indexed by <math>i</math> and <math>j</math>; <math>X</math> is the variable of interest; <math>\bar X</math> is the mean of <math>X</math>; <math>w_{ij}</math> is a matrix of spatial weights; and <math>W</math> is the sum of all <math>w_{ij}</math>.
 
The value of Geary's ''C'' lies between 0 and 2. 1 means no spatial autocorrelation. Values lower than 1 demonstrate increasing positive spatial autocorrelation, whilst values higher than 1 illustrate increasing negative spatial autocorrelation.
 
Geary's ''C'' is inversely related to [[Moran's I|Moran's ''I'']], but it is not identical. Moran's ''I'' is a measure of global spatial autocorrelation, while Geary's ''C'' is more sensitive to local spatial autocorrelation.
 
Geary's ''C'' is also known as Geary's contiguity ratio, Geary's ratio, or the Geary index.{{citation needed|date=March 2013}}
 
This statistic was developed by [[Roy C. Geary]].<ref>{{Cite journal
| doi = 10.2307/2986645
| author = [[Roy C. Geary|Geary, R. C.]]
| year = 1954
| title = The Contiguity Ratio and Statistical Mapping
| publisher = [[The Incorporated Statistician]]
| volume = 5
| pages = 115&ndash;145
| jstor = 2986645
| journal = The Incorporated Statistician
| issue = 3
}}</ref>
 
==Sources==
{{reflist}}
 
[[Category:Spatial data analysis]]
[[Category:Covariance and correlation]]
 
 
{{stats-stub}}

Revision as of 20:26, 26 November 2013

Template:Multiple issues Geary's C is a measure of spatial autocorrelation. Like temporal autocorrelation, spatial autocorrelation means that adjacent observations of the same phenomenon are correlated. However, temporal autocorrelation is about proximity in time, while spatial autocorrelation is about proximity in (multi-dimensional) space. Spatial autocorrelation is more complex than autocorrelation because the correlation is multi-dimensional and bi-directional.

Geary's C is defined as

C=(N1)ijwij(XiXj)22Wi(XiX¯)2

where N is the number of spatial units indexed by i and j; X is the variable of interest; X¯ is the mean of X; wij is a matrix of spatial weights; and W is the sum of all wij.

The value of Geary's C lies between 0 and 2. 1 means no spatial autocorrelation. Values lower than 1 demonstrate increasing positive spatial autocorrelation, whilst values higher than 1 illustrate increasing negative spatial autocorrelation.

Geary's C is inversely related to Moran's I, but it is not identical. Moran's I is a measure of global spatial autocorrelation, while Geary's C is more sensitive to local spatial autocorrelation.

Geary's C is also known as Geary's contiguity ratio, Geary's ratio, or the Geary index.Potter or Ceramic Artist Truman Bedell from Rexton, has interests which include ceramics, best property developers in singapore developers in singapore and scrabble. Was especially enthused after visiting Alejandro de Humboldt National Park.

This statistic was developed by Roy C. Geary.[1]

Sources

43 year old Petroleum Engineer Harry from Deep River, usually spends time with hobbies and interests like renting movies, property developers in singapore new condominium and vehicle racing. Constantly enjoys going to destinations like Camino Real de Tierra Adentro.


Template:Stats-stub

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